RESEARCH ON VOLTERRA NONLINEAR ADAPTIVE SYSTEMS AND FAST ADAPTICE ALGORITHMS

VOLTERRA非线性自适应系统及快速自适应算法研究

• 批准号: 12650395
• 负责人: CHAO Jinhui
• 金额: $ 1.73万
• 依托单位: CHUO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12650395/
• 关键词: NONLINEAR SYSTEMS; ADAPTIVE FILTERS; SIGNAL PROCESSING; VOLTERRA SYSTEMS; FAST ALGORITHM; RLS ALGORITHM; RLS アルゴリズム; LMS アルゴリズム; 適応フィルタ; Volterraフィルタ; 非線形フィルタ; 誤差曲面; 収束解析; 曲率解析; 高速算法

It is shown that the error surface of quadratic Volterra adaptive filters (ADF) is always extremely steep in one particular direction but relatively flat in the rest directions. This nontrivial geometry explains the instability in the learning processing of Volterra ADF and implies and unavoidable slow convergence of tradictional gradient adaptive algorithms. On the other hand, the RLS algorithm for Volterra ADF costs O(N^5) multiplications where N is the number of linear terms in the filter input. This paper presents a new algorithm for Gaussian input signals which converges in the same rate as RLS but costs only O(N^2) multiplications, the same order as the LMS algorithm. This algorithm is based on a complete analysis of the intrinsic geometry of the error surface for white input signals and whitening operation of colored input signals. Simulations shown that this algorithm works well also in non-Gaussian input cases.

结果表明，二次Volterra自适应滤波器(ADF)的误差面在某一特定方向上总是非常陡峭，而在其余方向上相对平坦。这种非平凡几何解释了Volterra ADF在学习过程中的不稳定性，并暗示了传统梯度自适应算法不可避免的缓慢收敛。另一方面，Volterra ADF的RLS算法需要O(N^5)次乘法，其中N是滤波器输入中的线性项数。本文提出了一种新的高斯输入信号的算法，它的收敛速率与RLS相同，但只需要O(N^2)次乘法，与LMS算法的阶数相同。该算法基于对白色输入信号误差面的内在几何特征和有色输入信号的白化操作的全面分析。仿真结果表明，该算法在非高斯输入情况下也能取得较好的效果。

项目成果

趙 晋輝, 宇野 晋平, 久保田 智規, 猪股 篤: "Volterra形非線形FIR適応フィルタの高速収束算法に関する考察"電子情報通信学会論文誌(A). Vol.J83-A No.4. 370-378 (2000)

赵金辉、Shinpei Uno、Tomoki Kubota、Atsushi Inomata：“Volterra型非线性FIR自适应滤波器的高速收敛算法研究”电子信息通信工程师学会学报（A）第J83-A号。 4. 370-378（2000）

J.Chao, T.Kubota, S.Uno: "Fast RLS adaptive algorithm of quadratic Volterra adaptive filters"Proceeding of the 2000 EUROSIPCO 2000. 142-145 (2000)

J.Chao、T.Kubota、S.Uno：“二次 Volterra 自适应滤波器的快速 RLS 自适应算法”Proceeding of the 2000 EUROSIPCO 2000. 142-145 (2000)

J. Chao, S. Uno, T. Kubota, A. Inomata: "Fast adaptive algorithms of Volterra FIR ADF"Transactions of IEICE. Vol. J82-A no. 4. 370-378 (2000)

J. Chao、S. Uno、T. Kubota、A. Inomata：“Volterra FIR ADF 的快速自适应算法”IEICE 交易。

J. Chao, M. Hoshino: "A Multilayer RBF network and its supervised learning""Neural Information Processing" Ed. by L. Zhang, F. Gu, Fudan Univ. Press, Proceeding ICONIP. Vol.3. 1366-1371 (2001)

J. Chao、M. Hoshino：“多层 RBF 网络及其监督学习”《神经信息处理》Ed。

K. Abe, T. Kubota, J. Chao: "Fast ELS algorithms of Volterra ADF with non Gaussian input signals"IEICE Society 2000 Conference. A-4-6. 97 (2000)

K. Abe、T. Kubota、J. Chao：“具有非高斯输入信号的 Volterra ADF 的快速 ELS 算法”IEICE Society 2000 会议。